Source Code for Chaotic Differential Evolution Algorithm

The Chaotic Differential Evolution Algorithm is an intelligent optimization technique that integrates chaos theory with differential evolution principles. This algorithm enhances population diversity through chaotic mapping, effectively addressing the issue of traditional differential evolution algorithms easily converging to local optima. In code implementation, key functions typically include chaos sequence generation, population initialization, and mutation operations with chaotic perturbations.

From an implementation perspective, the algorithm first utilizes chaotic sequences for population initialization, ensuring more uniform distribution of initial solutions across the search space. Compared to conventional random initialization, chaotic initialization provides better coverage of the entire solution space. In practical coding, this can be achieved using logistic maps or tent maps to generate chaotic sequences. During the mutation phase, the algorithm applies chaotic mapping to perturb mutation vectors, enhancing exploration capability. This perturbation strategy, often implemented through chaotic dynamic parameters, helps the algorithm escape local optima and improves global search performance.

The crossover operation preserves the classical differential evolution approach while incorporating a dynamic adjustment mechanism based on chaotic sequences. In code implementation, this typically involves adaptively modifying crossover probability using chaotic variables, balancing global exploration and local exploitation capabilities throughout the evolutionary process. The selection operation maintains the "survival of the fittest" principle, where superior individuals are retained for the next generation through straightforward comparison operations in the code.

This algorithm is particularly suitable for complex multimodal optimization problems and finds wide applications in function optimization and parameter tuning. By integrating chaos theory, the algorithm maintains the simplicity and effectiveness of differential evolution while significantly improving global convergence performance. For beginners, understanding the integration method between chaotic mapping and differential evolution - particularly the implementation of chaotic sequence generation and its application in population initialization and parameter control - is crucial for mastering this algorithm.